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X(13), X(14) A2 = Avertex of second Brocard triangle (singular focus) foot Ha of Aaltitude point at infinity of median AG 

We meet these three curves in "Orthocorrespondence and Orthopivotal Cubics" ยง6.5.1. See the FG paper "Orthocorrespondence and orthopivotal cubics" in the Downloads page and Orthopivotal cubics in the glossary. O(A) = K053A (figure above) is :
O(B) = K053B and O(C) = K053C have analogous properties obtained by cyclic permutations. These three strophoids generate the net formed by all the orthopivotal cubics and, in particular, the Neuberg cubic, the Brocard (second) cubic, Kn. The isotomic conjugation transforms O(A), O(B), O(C) into three concentric hyperbolas passing through X(298) and X(299), with center X(325) = isotomic conjugate of the Tarry point X(98). See also Paul Yiu's paper "Conic Construction of a Triangle from the Feet of Its Angle Bisectors" here. 
